Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

Confirmation of an exoplanet using the transit color signature: Kepler-418b, a blended giant planet in a multiplanet system

We announce confirmation of Kepler-418b, one of two proposed planets in this system. This is the first confirmation of an exoplanet based primarily on the transit color signature technique. We used the Kepler public data archive combined with multicolor photometry from the Gran Telescopio de Canarias and radial velocity follow-up using FIES at the Nordic Optical Telescope for confirmation. We report a confident detection of a transit color signature that can only be explained by a compact occulting body, entirely ruling out a contaminating eclipsing binary, a hierarchical triple, or a grazing eclipsing binary. Those findings are corroborated by our radial velocity measurements, which put an upper limit of ~1 Mjup on the mass of Kepler-418b. We also report that the host star is significantly blended, confirming the ~10% light contamination suspected from the crowding metric in the Kepler light curve measured by the Kepler team. We report detection of an unresolved light source that contributes an additional ~40% to the target star, which would not have been detected without multicolor photometric analysis. The resulting planet-star radius ratio is 0.110 +/- 0.0025, more than 25% more than the 0.087 measured by Kepler, leading to a radius of 1.20 +/- 0.16 Rjup instead of the 0.94 Rjup measured by the Kepler team. This is the first confirmation of an exoplanet candidate based primarily on the transit color signature, demonstrating that this technique is viable from ground for giant planets. It is particularly useful for planets with long periods such as Kepler-418b, which tend to have long transit durations. Additionally, multicolor photometric analysis of transits can reveal unknown stellar neighbors and binary companions that do not affect the classification of the transiting object but can have a very significant effect on the perceived planetary radius.Comment: accepted by Astronomy & Astrophysic

Kepler423b: a half-Jupiter mass planet transiting a very old solar-like star

We report the spectroscopic confirmation of the Kepler object of interest KOI-183.01 (Kepler-423b), a half-Jupiter mass planet transiting an old solar-like star every 2.7 days. Our analysis is the first to combine the full Kepler photometry (quarters 1-17) with high-precision radial velocity measurements taken with the FIES spectrograph at the Nordic Optical Telescope. We simultaneously modelled the photometric and spectroscopic data-sets using Bayesian approach coupled with Markov chain Monte Carlo sampling. We found that the Kepler pre-search data conditioned (PDC) light curve of KOI-183 exhibits quarter-to-quarter systematic variations of the transit depth, with a peak-to-peak amplitude of about 4.3 % and seasonal trends reoccurring every four quarters. We attributed these systematics to an incorrect assessment of the quarterly variation of the crowding metric. The host star KOI-183 is a G4 dwarf with $M_\star=0.85\pm0.04$ M_\rm{Sun}, $R_\star=0.95\pm0.04$ R_\rm{Sun}, $T_\mathrm{eff}=5560\pm80$ K, $[M/H]=-0.10\pm0.05$ dex, and with an age of $11\pm2$ Gyr. The planet KOI-183b has a mass of $M_\mathrm{p}=0.595\pm0.081$ M$_\mathrm{Jup}$ and a radius of $R_\mathrm{p}=1.192\pm0.052$ R$_\mathrm{Jup}$, yielding a planetary bulk density of $\rho_\mathrm{p}=0.459\pm0.083$ g/cm$^{3}$. The radius of KOI-183b is consistent with both theoretical models for irradiated coreless giant planets and expectations based on empirical laws. The inclination of the stellar spin axis suggests that the system is aligned along the line of sight. We detected a tentative secondary eclipse of the planet at a 2-$\sigma$ confidence level ($\Delta F_{\mathrm{ec}}=14.2\pm6.6$ ppm) and found that the orbit might have a small non-zero eccentricity of $e=0.019^{+0.028}_{-0.014}$. With a Bond albedo of $A_\mathrm{B}=0.037\pm0.019$, KOI-183b is one of the gas-giant planets with the lowest albedo known so far.Comment: 13 pages, 13 figures, 5 tables. Accepted for publication in A&A. Planet designation changed from KOI-183b to Kepler-423

High angular resolution imaging and infrared spectroscopy of CoRoT candidates

Studies of transiting extrasolar planets are of key importance for understanding the nature of planets outside our solar system because their masses, diameters, and bulk densities can be measured. An important part of transit-search programmes is the removal of false-positives. The critical question is how many of the candidates that passed all previous tests are false positives. For our study we selected 25 CoRoT candidates that have already been screened against false-positives using detailed analysis of the light curves and seeing-limited imaging, which has transits that are between 0.7 and 0.05% deep. We observed 20 candidates with the adaptive optics imager NaCo and 18 with the high-resolution infrared spectrograph CRIRES. We found previously unknown stars within 2 arcsec of the targets in seven of the candidates. All of these are too faint and too close to the targets to have been previously detected with seeing-limited telescopes in the optical. Our study thus leads to the surprising results that if we remove all candidates excluded by the sophisticated analysis of the light-curve, as well as carrying out deep imaging with seeing-limited telescopes, still 28-35% of the remaining candidates are found to possess companions that are bright enough to be false-positives. Given that the companion-candidates cluster around the targets and that the J-K colours are consistent with physical companions, we conclude that the companion-candidates are more likely to be physical companions rather than unrelated field stars.Comment: 12 pages, 12 figures, A&A in pres

Transiting exoplanets from the CoRoT space mission. XV. CoRoT-15b: a brown dwarf transiting companion

We report the discovery by the CoRoT space mission of a transiting brown dwarf orbiting a F7V star with an orbital period of 3.06 days. CoRoT-15b has a radius of 1.12 +0.30 -0.15 Rjup, a mass of 63.3 +- 4.1 Mjup, and is thus the second transiting companion lying in the theoretical mass domain of brown dwarfs. CoRoT-15b is either very young or inflated compared to standard evolution models, a situation similar to that of M-dwarfs stars orbiting close to solar-type stars. Spectroscopic constraints and an analysis of the lightcurve favors a spin period between 2.9 and 3.1 days for the central star, compatible with a double-synchronisation of the system.Comment: 7 pages, 6 figures, accepted in A&

Deep MMT Transit Survey of the Open Cluster M37 IV: Limit on the Fraction of Stars With Planets as Small as 0.3 R_J

We present the results of a deep (15 ~< r ~< 23), 20 night survey for transiting planets in the intermediate age open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5m MMT. We do not detect any transiting planets among the ~1450 observed cluster members. We do, however, identify a ~ 1 R_J candidate planet transiting a ~ 0.8 Msun Galactic field star with a period of 0.77 days. The source is faint (V = 19.85 mag) and has an expected velocity semi-amplitude of K ~ 220 m/s (M/M_J). We conduct Monte Carlo transit injection and recovery simulations to calculate the 95% confidence upper limit on the fraction of cluster members and field stars with planets as a function of planetary radius and orbital period. Assuming a uniform logarithmic distribution in orbital period, we find that < 1.1%, < 2.7% and < 8.3% of cluster members have 1.0 R_J planets within Extremely Hot Jupiter (EHJ, 0.4 < T < 1.0 day), Very Hot Jupiter (VHJ, 1.0 < T < 3.0 days) and Hot Jupiter (HJ, 3.0 < T < 5.0 days) period ranges respectively. For 0.5 R_J planets the limits are < 3.2%, and < 21% for EHJ and VHJ period ranges, while for 0.35 R_J planets we can only place an upper limit of < 25% on the EHJ period range. For a sample of 7814 Galactic field stars, consisting primarily of FGKM dwarfs, we place 95% upper limits of < 0.3%, < 0.8% and < 2.7% on the fraction of stars with 1.0 R_J EHJ, VHJ and HJ assuming the candidate planet is not genuine. If the candidate is genuine, the frequency of ~ 1.0 R_J planets in the EHJ period range is 0.002% < f_EHJ < 0.5% with 95% confidence. We place limits of < 1.4%, < 8.8% and < 47% for 0.5 R_J planets, and a limit of < 16% on 0.3 R_J planets in the EHJ period range. This is the first transit survey to place limits on the fraction of stars with planets as small as Neptune.Comment: 61 pages, 19 figures, 5 tables, replaced with the version accepted for publication in Ap

HAT-P-11b: A Super-Neptune Planet Transiting a Bright K Star in the Kepler Field

We report on the discovery of HAT-P-11b, the smallest radius transiting extrasolar planet (TEP) discovered from the ground, and the first hot Neptune discovered to date by transit searches. HAT-P-11b orbits the bright (V=9.587) and metal rich ([Fe=H] = +0.31 +/- 0.05) K4 dwarf star GSC 03561-02092 with P = 4.8878162 +/- 0.0000071 days and produces a transit signal with depth of 4.2 mmag. We present a global analysis of the available photometric and radial-velocity data that result in stellar and planetary parameters, with simultaneous treatment of systematic variations. The planet, like its near-twin GJ 436b, is somewhat larger than Neptune (17Mearth, 3.8Rearth) both in mass Mp = 0.081 +/- 0.009 MJ (25.8 +/- 2.9 Mearth) and radius Rp = 0.422 +/- 0.014 RJ (4.73 +/- 0.16 Rearth). HAT-P-11b orbits in an eccentric orbit with e = 0.198 +/- 0.046 and omega = 355.2 +/- 17.3, causing a reflex motion of its parent star with amplitude 11.6 +/- 1.2 m/s, a challenging detection due to the high level of chromospheric activity of the parent star. Our ephemeris for the transit events is Tc = 2454605.89132 +/- 0.00032 (BJD), with duration 0.0957 +/- 0.0012 d, and secondary eclipse epoch of 2454608.96 +/- 0.15 d (BJD). The basic stellar parameters of the host star are M* = 0.809+0.020-0.027 Msun, R* = 0.752 +/- 0.021 Rsun and Teff = 4780 +/- 50 K. Importantly, HAT-P-11 will lie on one of the detectors of the forthcoming Kepler mission. We discuss an interesting constraint on the eccentricity of the system by the transit light curve and stellar parameters. We also present a blend analysis, that for the first time treats the case of a blended transiting hot Jupiter mimicing a transiting hot Neptune, and proves that HAT-P-11b is not such a blend.Comment: Accepted for publication in ApJ, 24 pages, 14 figures, 6 tables. All RV data presented in this versio

Transit Photometry as an Exoplanet Discovery Method

Photometry with the transit method has arguably been the most successful exoplanet discovery method to date. A short overview about the rise of that method to its present status is given. The method's strength is the rich set of parameters that can be obtained from transiting planets, in particular in combination with radial velocity observations; the basic principles of these parameters are given. The method has however also drawbacks, which are the low probability that transits appear in randomly oriented planet systems, and the presence of astrophysical phenomena that may mimic transits and give rise to false detection positives. In the second part we outline the main factors that determine the design of transit surveys, such as the size of the survey sample, the temporal coverage, the detection precision, the sample brightness and the methods to extract transit events from observed light curves. Lastly, an overview over past, current and future transit surveys is given. For these surveys we indicate their basic instrument configuration and their planet catch, including the ranges of planet sizes and stellar magnitudes that were encountered. Current and future transit detection experiments concentrate primarily on bright or special targets, and we expect that the transit method remains a principal driver of exoplanet science, through new discoveries to be made and through the development of new generations of instruments.Comment: Review chapte

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first Super-Earth with measured radius

We report the discovery of very shallow (DF/F = 3.4 10-4), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as due to the presence of a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We use CoRoT color information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy and preliminary results from Radial Velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star are derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. We examine carefully all conceivable cases of false positives, and all tests performed support the planetary hypothesis. Blends with separation larger than 0.40 arcsec or triple systems are almost excluded with a 8 10-4 risk left. We conclude that, as far as we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 10-5 day and a radius of Rp = 1.68 +/- 0.09 REarth. Analysis of preliminary radial velocity data yields an upper limit of 21 MEarth for the companion mass, supporting the finding. CoRoT-7b is very likely the first Super-Earth with a measured radius.Comment: Accepted in Astronomy and Astrophysics; typos and language corrections; version sent to the printer w few upgrade

Bayesian Methods for Exoplanet Science

Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources. Combining repeated observations of periodic events, simultaneous observations with multiple telescopes, different observation techniques, and existing information from theory and prior research can help to disentangle the systematics from the planetary signals, and offers synergistic advantages over analysing observations separately. Bayesian inference provides a self-consistent statistical framework that addresses both the necessity for complex systematics models, and the need to combine prior information and heterogeneous observations. This chapter offers a brief introduction to Bayesian inference in the context of exoplanet research, with focus on time series analysis, and finishes with an overview of a set of freely available programming libraries.Comment: Invited revie